• Korean Journal of Mathematics
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• 제31권1호
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• pp.35-48
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• 2023

Let 𝔼 be a CAT(0) space and K be a nonempty closed convex subset of 𝔼. Let T : K → 𝓟(K) be a multimap such that F(T) ≠ ∅ and ℙ_T(x) = {y ∈ Tx : d(x, y) = d(x, Tx)}. Define sequence {x_n} by x_n+1 = (1 - α)𝜈_n⊕αw_n, y_n = (1 - β)u_n⊕βw_n, z_n = (1-γ)x_n⊕γu_n where α, β, γ ∈ [0; 1]; u_n ∈ ℙ_T (x_n); 𝜈_n ∈ ℙ_T (y_n) and w_n ∈ ℙ_T (z_n). (1) If ℙ_T is quasi-nonexpansive, then it is proved that {x_n} converges strongly to a fixed point of T. (2) If a multimap T satisfies Condition(I) and ℙ_T is quasi-nonexpansive, then {x_n} converges strongly to a fixed point of T. (3) Finally, we establish a weak convergence result. Our results extend and unify some of the related results in the literature.

• 대한수학회보
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• 제58권6호
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• pp.1387-1400
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• 2021

Suppose that $T=\(\array{A&0\\U&B}\)$ is a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. Let ℭ₁ and ℭ₂ be two classes of left A-modules, 𝔇₁ and 𝔇₂ be two classes of left B-modules. We prove that (ℭ₁, ℭ₂) and (𝔇₁, 𝔇₂) are admissible balanced pairs if and only if (p(ℭ₁, 𝔇₁), h(ℭ₂, 𝔇₂) is an admissible balanced pair in T-Mod. Furthermore, we describe when ($P^{C_1}_{D_1}$, $I^{C_2}_{D_2}$) is an admissible balanced pair in T-Mod. As a consequence, we characterize when T is a left virtually Gorenstein ring.

• 호남수학학술지
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• 제45권4호
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• pp.598-609
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• 2023

The purpose of this article is to obtain the spectrum, fine spectrum, approximate point spectrum, defect spectrum and compression spectrum of the double band matrix U (a₀, a₁, a₂; b₀, b₁, b₂), b₀, b₁, b₂≠0 on the sequence space ℓ_p (1 < p < ∞).

• 마이크로전자및패키징학회지
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• 제30권4호
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• pp.79-85
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• 2023

(1-4x)Bi_1.5Zn_1.0Nb_1.5O₇-3xBi₂Zn_2/3Nb_4/3O₇-2xLiZnNbO₄(x=0.03-0.21) 조성의 새로운 저온 동시 소성 세라믹(LTCC) 유전체는 Bi_1.5Zn_1.0Nb_1.5O₇-xLi₂CO₃(x=0.03-0.21) 혼합물을 850℃~920℃에서 4 시간 반응성 액상소결(reactive liquid phase sintering)을 하여 제조하였다. 소결이 진행되는 동안 Li₂CO₃는 Bi_1.5Zn_1.0Nb_1.5O₇과 반응하여 Bi₂Zn_2/3Nb_4/3O₇과 LiZnNbO₄를 생성하였고 얻어진 소결체의 상대 소결밀도는 이론 밀도의 96% 이상이었다. 초기 Li₂CO₃ 함량(x)을 조절하여 최종 소결체내에 존재하는 Bi_1.5Zn_1.0Nb_1.5O₇, Bi₂Zn_2/3Nb_4/3O₇ 및 LiZnNbO₄ 상의 상대적인 함량을 제어함으로써 높은 유전율(ε_r), 낮은 유전손실(tan δ) 및 NP0 특성(TCε ≤ ±30 ppm/℃)의 유전율 온도계수(TCε)를 갖는 유전체를 개발할 수 있었다. Li₂CO₃의 첨가가 x=0.03 mol에서 x=0.15 mol로 증가함에 따라 얻어진 복합체 내의 Bi₂Zn_2/3Nb_4/3O₇와 LiZnNbO₄의 부피 분율은 증가하였고, Bi_1.5Zn_1.0Nb_1.5O₇의 부피 분율은 감소하였다. 그 결과 복합체의 유전율(ε_r)은 148.38에서 126.99로 유전손실(tan δ)은 5.29×10^-4에서 3.31×10^-4로 그리고 유전율 온도계수(TCε)는 -340.35 ppm/℃에서 299.67 ppm/℃로 변화되었다. NP0 특성을 갖는 유전체는 Li₂CO₃의 함량이 x=0.09일 때 얻을 수 있었고, 이 때의 유전율(ε_r)은 143.06, 유전손실(tan δ)값은 4.31×10^-4, 그리고 유전율 온도계수(TCε)값은 -9.98 ppm/℃ 이었다. Ag전극과의 화학적 호환성 실험은 개발된 복합 재료는 Ag 전극과 동시 소성 과정에서 전극과 반응이 없음을 보여주었다.

• 대한수학회보
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• 제60권6호
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• pp.1651-1672
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• 2023

In 2010, Li-Ye [13, Theorem 0.1] proved that P(ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), Γ"(z)) ≢ 0 in ℂ, where m is a non-negative integer, and P(u₀, u₁, . . . , u_m, v₀, v₁, v₂) is any non-trivial polynomial in its arguments with coefficients in the field ℂ. Later on, Li-Ye [15, Theorem 1] proved that P(z, Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z), ζ(z)) ≢ 0 in z ∈ ℂ for any non-trivial distinguished polynomial P(z, u₀, u₁, . . ., u_n, v) with coefficients in a set L_δ of the zero function and a class of nonzero functions f from ℂ to ℂ ∪ {∞} (cf. [15, Definition 1]). In this paper, we prove that P(z, ζ(z), ζ'(z), . . . , ζ^(m)(z), Γ(z), Γ'(z), . . . , Γ⁽ⁿ⁾(z)) ≢ 0 in z ∈ ℂ, where m and n are two non-negative integers, and P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is any non-trivial polynomial in the m + n + 2 variables u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n with coefficients being meromorphic functions of order less than one, and the polynomial P(z, u₀, u₁, . . . , u_m, v₀, v₁, . . . , v_n) is a distinguished polynomial in the n + 1 variables v₀, v₁, . . . , v_n. The question studied in this paper is concerning the conjecture of Markus from [16]. The main results obtained in this paper also extend the corresponding results from Li-Ye [12] and improve the corresponding results from Chen-Wang [5] and Wang-Li-Liu-Li [23], respectively.

• 한국재료학회지
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• 제34권4호
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• pp.185-193
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• 2024

In this study, NASICON-type Li_1+XGa_XTi_2-X(PO₄)₃ (x = 0.1, 0.3 and 0.4) solid-state electrolytes for all-solid-state batteries were synthesized through the sol-gel method. In addition, the influence on the ion conductivity of solid-state electrolytes when partially substituted for Ti⁴⁺ (0.61Å) site to Ga³⁺ (0.62Å) of trivalent cations was investigated. The obtained precursor was heat treated at 450 ℃, and a single crystalline phase of Li_1+XGa_XTi_2-X(PO₄)₃ systems was obtained at a calcination temperature above 650 ℃. Additionally, the calcinated powders were pelletized and sintered at temperatures from 800 ℃ to 1,000 ℃ at 100 ℃ intervals. The synthesized powder and sintered bodies of Li_1+XGa_XTi_2-X(PO₄)₃ were characterized using TG-DTA, XRD, XPS and FE-SEM. The ionic conduction properties as solid-state electrolytes were investigated by AC impedance. As a result, Li_1+XGa_XTi_2-X(PO₄)₃ was successfully produced in all cases. However, a GaPO₄ impurity was formed due to the high sintering temperatures and high Ga content. The crystallinity of Li_1+XGa_XTi_2-X(PO₄)₃ increased with the sintering temperature as evidenced by FE-SEM observations, which demonstrated that the edges of the larger cube-shaped grains become sharper with increases in the sintering temperature. In samples with high sintering temperatures at 1,000 ℃ and high Ga content above 0.3, coarsening of grains occurred. This resulted in the formation of many grain boundaries, leading to low sinterability. These two factors, the impurity and grain boundary, have an enormous impact on the properties of Li_1+XGa_XTi_2-X(PO₄)₃. The Li_1.3Ga_0.3Ti_1.7(PO₄)₃ pellet sintered at 900 ℃ was denser than those sintered at other conditions, showing the highest total ion conductivity of 7.66 × 10^-5 S/cm at room temperature. The total activation energy of Li-ion transport for the Li_1.3Ga_0.3Ti_1.7(PO₄)₃ solid-state electrolyte was estimated to be as low as 0.36 eV. Although the Li_1+XGa_XTi_2-X(PO₄)₃ sintered at 1,000 ℃ had a relatively high apparent density, it had less total ionic conductivity due to an increase in the grain-boundary resistance with coarse grains.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.123-129
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• 2023

For an ordered set W = {w₁, w₂, . . . , w_k} of vertices and a vertex v in a connected graph G, the k-vector r(v|W) = (d(v, w₁), d(v, w₂), . . . , d(v, w_k)) is called the metric representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct metric representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension dim(G), and a resolving set of minimum cardinality is a basis of G. The corona product, G ⊙ H of graphs G and H is obtained by taking one copy of G and n(G) copies of H, and by joining each vertex of the ith copy of H to the ith vertex of G. In this paper, we obtain bounds for dim(G ⊙ K₁), characterize all graphs G with dim(G ⊙ K₁) = dim(G), and prove that dim(G ⊙ K₁) = n - 1 if and only if G is the complete graph K_n or the star graph K_1,n-1.

• The Korean Journal of Physiology and Pharmacology
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• 제25권6호
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• pp.525-532
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• 2021

We have investigated the relative roles of α₁-adrenoceptors and purinoceptors in contractions to low and high frequency stimulation of the mouse vas deferens, in terms of the time course of responses. In separate experiments, isometric contractile responses were obtained to 10 pulses at 1 Hz and 40 pulses at 10 Hz. Responses to 1 Hz stimulation consisted of a series of discrete peaks. The α_1A-adrenoceptor antagonist RS100329 (10^-9M-10^-7M) significantly reduced the response to the first pulse, the α_1D-adrenoceptor antagonist BMY7378 (10^-7M-10^-6M) significantly reduced the response to the first two pulses, and the non-selective α₁-adrenoceptor antagonist prazosin (10^-8M) reduced the response to the first 4 pulses at 1 Hz. Responses to 10 Hz stimulation consisted of an early peak response and a maintained plateau response. RS100329 significantly reduced the peak response but did not significantly affect the plateau response. Prazosin, significantly reduced both the peak and plateau responses. The α_1A-adrenoceptor antagonist RS17053 in high concentrations reduced mainly the plateau response leaving a clear early peak response. The plateau response of contraction was almost abolished by the purinoceptor antagonist suramin. These results suggest that there is a relatively minor early α_1D-adrenoceptor and a larger early α_1A-adrenoceptor component to stimulationevoked contractions of mouse vas deferens, but the major α₁-adrenoceptor component is revealed by prazosin to be α_1B-adrenoceptor mediated. α_1B-Adrenoceptor activation probably facilitates contractions mediated by other α₁-adrenoceptors and by purinoceptors. These results suggest that combined non-selective α₁-adrenoceptor blockade, particularly α_1B-adrenoceptor blockade, in addition to P2X1-purinoceptor blockade is useful in reducing male fertility.

• Journal of the Korean Wood Science and Technology
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• 제50권4호
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• pp.219-236
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• 2022

Wood-based nanocomposite electrode materials were synthesized for application in supercapacitors by mixing nanostructured hematite (Fe₂O₃) with highly porous activated carbon (AC) produced from the wood-waste of Pinus roxburghii. The AC was characterized using various instrumental techniques and the results showed admirable electrochemical properties, such as high surface area and reasonable porosity. Firstly, AC was tested as an electrode material for supercapacitors and it showed a specific capacitance of 59.02 Fg^-1 at a current density of 1 Ag^-1, cycle life of 84.2% after 1,000 cycles (at a current density of 3 Ag^-1), and energy density of 5.1 Wh/kg at a power density of 135 Wkg^-1. However, when the AC was composited with different ratios of Fe₂O₃ (1:1, 2:1, and 1:2), there was an overall improvement in its electrochemical performance. Among the 3 ratios, 2:1 (AC:Fe₂O₃) had the best specific capacitance of 102.42 Fg^-1 at 1 Ag^-1, cycle life of 94.4% capacitance after 1,000 cycles (at a current density of 3 Ag^-1), and energy density of 8.34 Wh/kg at a power density of 395.15 Wkg^-1 in 6 M KOH electrolyte in a 3-electrode experimental setup with a high working voltage of 1.55 V. Furthermore, when Fe₂O₃ was doubled, 1:2 (AC:Fe₂O₃), the electrochemical capacitive performance of the electrode twisted and deteriorated due to either the accumulation of Fe₂O₃ particles within the composite or higher bulk resistance value of pure Fe₂O₃.

• 충청수학회지
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• 제33권2호
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• pp.227-236
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• 2020

A set {a₁, a₂,_…, a_m} of positive integers is called Diophantine m-tuple if a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of torsion group of elliptic curve E_k constructed by Diophantine triple, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1.